Researchers at the University of Illinois at Urbana-Champaign have developed a unique single-step process to achieve three-dimensional (3D) texturing of graphene and graphite. Using a commercially available ...

Scientists are using biology to improve the properties of lithium ion batteries. Researchers at the University of Maryland, Baltimore County (UMBC) have isolated a peptide, a type of biological molecule, ...

By dipping small pieces of an ordinary kitchen sponge into solutions of nanoscale electrode materials, scientists have created a light-weight, low-cost supercapacitor that benefits from the sponge's porous ...

Northwestern University scientists are the first to develop a catalyst that can perform a remarkable feat found only in nature: take nitrogen from the air and turn it into ammonia under natural conditions. No high temperatures ...

(Phys.org)—A team of researchers with members from Czech Republic and Germany has found that the general explanation given to high school chemistry students regarding the reasons for an explosion when alkali ...

A research team at KAIST has developed a method to form micropores of less than 2 nanometers within porous polymers where 10 nanometers long mesopores connect like a net. The advantage of the porous polymers ...

A new catalyst could have dramatic environmental benefits if it can live up to its potential, suggests research from Singapore. A*STAR researchers have produced a catalyst with gold-nanoparticle antennas ...

Hydrocarbons continue to be our primary source of energy. However, they do not necessarily have to come from fossil sources. Why not reverse the combustion process to make the hydrocarbons from CO2? This could ...

Last week, US tech giants Google made a splash in the media, announcing plans to develop new 'disease-detecting magnetic nanoparticles'. This was almost universally welcomed – after all, trying to detect ...

When someone crumples a sheet of paper, that usually means it's about to be thrown away. But researchers have now found that crumpling a piece of graphene "paper"—a material formed by bonding together layers ...

Georgia Institute of Technology researchers have developed a novel method for improving silicon-based sensors used to detect biochemicals and other molecules in liquids. The simplified approach produces micro-scale ...

Conventional photovoltaic technology uses large, heavy, opaque, dark silicon panels, but this could soon change. The IK4-Ikerlan research centre is working with the UPV/EHU-University of the Basque Country ...

Surface area

Surface area is the measure of how much exposed area a solid object has, expressed in square units. Mathematical description of the surface area is considerably more involved then the definition of arc length of a curve. For polyhedra (objects with flat polygonal faces) the surface area is the sum of the areas of its faces. Smooth surfaces, such as a sphere, are assigned surface area using their representation as parametric surfaces. This definition of the surface area is based on methods of infinitesimal calculus and involves partial derivatives and double integration.

General definition of surface area was sought by Henri Lebesgue and Hermann Minkowski at the turn of the twentieth century. Their work led to the development of geometric measure theory which studies various notions of surface area for irregular objects of any dimension. An important example is the Minkowski content of a surface.